Question : An athlete runs 8 times around a circular field of radius 7 m in 3 minutes 40 seconds. His speed (in km/hr) is:
(Take $\pi=\frac{22}{7}$ )
Option 1: $\frac{72}{25}$
Option 2: $\frac{118}{25}$
Option 3: $\frac{144}{25}$
Option 4: $\frac{108}{25}$
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Correct Answer: $\frac{144}{25}$
Solution :
The distance covered by the athlete is the circumference of the circular field multiplied by the number of times he runs around it.
The circumference (C) of a circle, $C = 2\pi r$ where r is the radius of the circle.
Given:
r = 7 m
Number of rounds = 8
Substituting these values into the formula,
Total Distance = 8 × 2 × $\frac{22}{7}$ × 7 = 352 m
The time taken by the athlete is 3 minutes 40 seconds = 220 seconds.
$\text{Speed} = \frac{\text{Total Distance}}{\text{Time}} = \frac{352}{220} \, \text{m/s}$
$\text{Speed} = \frac{352}{220} \, \text{m/s} \times \frac{18}{5} \, \text{km/hr} = \frac{144}{25} \, \text{km/hr} $
Hence, the correct answer is $\frac{144}{25}$.
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